‘Knitting Is Coding’ and Yarn Is Programmable in This Physics Lab ‘Knitting Is Coding’ and Yarn Is Programmable in This Physics Lab

Some of the oldest examples date to the 11th century in Egypt. But despite generations of practical and experiential knowledge, the physical and mathematical properties of knitted fabric rarely are studied in a way that produces predictive models about how such fabrics behave.

Dr. Matsumoto argues that “knitting is coding” and that yarn is a programmable material. The potential dividends of her research range from wearable electronics to tissue scaffolding.

During the happy-hour meetup, she knitted a swatch illustrating a plastic surgery technique called Z-plasty. The swatch was for a talk she would deliver at 8 a.m. on Wednesday morning called “Twisted Topological Tangles.” Scores of physicists turned up, despite a competing parallel session on “The Extreme Mechanics of Balloons.”

“I’ve been knitting since I was a kid,” Dr. Matsumoto told her (mostly male) audience. “That was the thing I did to get along with my mom when I was a teenager. It’s just been a dream to take all of this stuff that I learned and played with as a child and turn it into something scientifically rigorous.”

As a first step, her team is enumerating all possible knittable stitches: “We know there’s going to be uncountably many, there’s going to be a countably infinite number. How to classify them is what we are working on now.”

[Like the Science Times page on Facebook. | Sign up for the Science Times newsletter.]

The investigation is informed by the mathematical tradition of knot theory. A knot is a tangled circle — a circle embedded with crossings that cannot be untangled. (A circle with no crossings is an “unknot.”)

“The knitted stitch is a whole series of slipknots, one after the other,” said Dr. Matsumoto. Rows and columns of slipknots form a lattice pattern so regular that it is analogous to crystal structure and crystalline materials.

By way of knot theory, Dr. Matsumoto essentially is developing a knit theory: an alphabet of unit-cell stitches, a glossary of stitch combinations, and a grammar governing the knitted geometry and topology — the fabric’s stretchiness, or its “emergent elasticity.”

How ‘floofy’ is it?

When discussing the emergent properties of knitting, Dr. Matsumoto sometimes makes reference to a butterfly, the vibrant blue morpho. Its color is optically emergent, the result not of chemical pigment but of structure. In effect, each wing is a metamaterial: covered in layers of nanosized scales, arranged in a pattern called a gyroid surface, the wing absorbs most wavelengths of light, but reflects blue.

Knitted fabric is also a metamaterial. A length of yarn is all but inelastic, but when configured in slipknots — in patterns of knits and purls — varying degrees of elasticity emerge.

“Just based on these two stitches, these two fundamental units, we can make a whole series of fabrics, and each of these fabrics has remarkably different elastic properties,” Dr. Matsumoto told the audience.

She first combined her math-y and woolly mind-sets as a Ph.D. student, after admiring a friend’s crocheted interpretation of the hyperbolic plane (curly kale is a vegetable example) and wondering how to do it differently.

“It irritated me that it wasn’t isotropic,” she recalled on the day before her talk. She could see where the crochet had begun, whereas a true hyperbolic plane should betray no starting point and no direction.

She thought, “I can fix that.”